Pep Guardiola's side have already broken the British transfer record to sign Jack Grealish from Aston Villa for £100m, but the City boss has confirmed his side's interest in Kane.
Spurs chairman Daniel Levy was originally thought to want £160m to reluctantly sanction the 28-year-old's departure, but a recent report claimed that he may be prepared to accept a fee closer to £140m.
Now, the Evening Standard claims that City are 'convinced' they can strike a deal in the region of £150m for Kane, who has now reported back for training ahead of the new season.
The report adds that Guardiola's side may not be able to sign the England captain before the season kicks off but are very optimistic that he will be donning the sky blue shirt by the end of the month.
Tottenham are reported to be making progress in their efforts to sign £60m-rated Lautaro Martinez from Inter Milan, but the Argentine would supposedly be a strike partner for Kane rather than a replacement.
Kane boasts 221 goals from 336 games in a Tottenham shirt, with 166 of those strikes coming in the Premier League, but he is yet to win a major trophy with the Lilywhites.